Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
388 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C3×C4×Dic7 | C4 | semidirect |
| 15. Dic7⋊Dic3 | C4 | direct (N × H) |
| 44. C4×Dic7 | Dic3 | semidirect |
| 55. C3×C4×C7 | C4⋊C4 | semidirect |
| 58. C3×Dic7 | C42 | semidirect |
| 100. C4×C7 | C4⋊Dic3 | semidirect |
| 103. Dic7 | C4×Dic3 | semidirect |
| 118. C3×C7 | C4×C4⋊C4 | semidirect |
| 140. C3×C4 | Dic7⋊C4 | semidirect |
| 157. C7 | C4×C4⋊Dic3 | semidirect |
| 172. C4 | Dic7⋊Dic3 | direct (N × H) |
| 173. C3 | C4×Dic7⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×C4×Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| #10620529 | 2 |
| C4×Dic7⋊C4 | 3 |
| C4×C4⋊Dic3 | 7 |